An operative environment is called strategic if it involves self interested agents who act on the basis of their own self interest (e.g. humans, organizations, companies) and their decisions affect each other. Decisions on how to act in strategic environments are taken by numerous organizations and individuals on a regular basis. Such decisions are referred to as “strategic decisions”.
When making strategic decisions, a decision maker needs to carefully consider not only his own action but the action of other decision makers that will act in response to the decision maker. Such situations arise in domains such as economic competition between companies where each company is after its own revenue, political situations, workforce management, and many more.
Game theory is a mathematical discipline that aims at shedding light on strategic decision making. Yet there is a large gap between modeling and analyzing real life situations and the tools that the theory currently provides.
Strategic games, or simply games, in game theory may be modeled using normal-form. A game in normal-form is a structure G=P, S, F, where P=1, 2, . . . , m) is a set of actors, S=(S1, S2, . . . , Sm) is an m-tuple of pure strategy sets, one for each actor, where each strategy set comprises a finite number of strategies that the actor may take, and where F=(F1, F2, . . . , Fm) is an m-tuple of payoff functions, where each payoff function Fi: S1×S2× . . . ×Sm is associated with an actor and defines the payoff of the actor based on the strategies taken by each actor.
Games in game theory may be modeled using game trees. Inner nodes of the trees represent strategic decisions by an actor, where all sibling nodes are associated with the same actor (i.e., strategic entity), and utilities (e.g., payoffs) are indicated in the leaf nodes. In a common game tree, each hierarchical level in the tree is associated with a different actor.